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Three Planet Galaxy and Stock Market Chaos


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#1 BMAD

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Posted 28 January 2014 - 10:18 PM

A galaxy consists of three planets, each of them moving along a straight line with its own constant speed. If the centers of all three planets happen to lie on a straight line (some kind of eclipse) the inhabitants of each planet go nuts (they cannot see their two neighbor planets all at once), start talking about the end of the world, and the stock market crashes. Show that there will be no more than two such market crashes on each of these planets.


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#2 dgreening

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Posted 02 February 2014 - 04:06 PM

This is not getting a lot of attention, so I am going to jump in. 

 

I think there must be something I am missing.

 

If the paths are no coplanar, then I don't think there are positions that will support 2 alignments.

 

Let's simplify the problem, by making the paths of the 3 planets coplanar.

 

If the 3 paths are parallel, then I think there can be only 1 point in time/ space that they will line up -- after that, they will never be in alignment again.

 

If we imagine that the paths of the 3 planets intersect and that the planets are travelling on paths as follow [I can't figure out how to post a picture that I created, so I am going to revert to compass points for ease of illustration]:

  • "Green" planet is travelling due east [90 degrees] towards the point of intersection

  • "Red"  planet is travelling due ESE  [120 degrees] towards the point of intersection

  • "Black"  planet is travelling ENE  [60 degrees] towards the point of intersection

If they line up before the intersection, there is a possibility that they will line up again after the intersection. After that, they will continue to diverge.

 

This second alignment requires just the right mix of relative speeds [probably Green is the middle speed while one of the others is faster and one is slower..

 

Not really a proof, but I think that is the answer. [sorry about having to revert to compass points].


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#3 bonanova

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Posted 03 February 2014 - 11:49 AM

Spoiler for more thoughts


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#4 bonanova

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Posted 03 February 2014 - 03:06 PM

Spoiler for Final thoughts

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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